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Spontaneous mechanical and energetic state transitions during Caenorhabditis elegans gastrulation

Gastrulation, namely cell internalization, is a significant milestone during the development of metazoans from worm to human, which generates multiple embryonic layers with distinct cell fates and spatial organizations. Although many molecular activities are known to facilitate this process, in this paper, we focus on gastrulation of the nematode Caenorhabditis elegans and theoretically demonstrate that even a group of cells with only isotropic repulsive and attractive interactions can experience such internalization behavior when dividing within a confined space. As the cell number increases and cell size decreases, the cells contacted to the eggshell become closer to each other along with harder lateral compression, and a cell that internalizes could effectively increase the cell neighbor distance and lower the potential energy of the system. The multicellular structure transits from single- to double-layer spontaneously with bistable states existing from 15- to 44-cell stages, near the gastrulation timing in vivo. Specifically, the cells with a larger size or placed near a smaller-curvature boundary are easier to internalize. Actively regulating a few cells' internalizations can make the morphogenesis noise-resistant. Our work successfully recaptures the key characteristics in C. elegans gastrulation and provides a rational interpretation of how this phenomenon emerges and is optimally programmed.